Question

a reaction has the general rate law, rate = kab^3. if the concentration of b is tripled, by what factor will the rate increase? 27 9 3 18

Explanation:

Step1: Substitute new concentration

Let the original rate be \( rate_1 = k[A][B]^3 \). When the concentration of \( B \) is tripled (\([B]_2 = 3[B]_1\)), the new rate \( rate_2=k[A][B]_2^3\).

Step2: Calculate the ratio of rates

Substitute \([B]_2 = 3[B]_1\) into \( rate_2\): \( rate_2=k[A](3[B]_1)^3\). Expand \((3[B]_1)^3 = 27[B]_1^3\). So \( rate_2 = 27k[A][B]_1^3\). Since \( rate_1 = k[A][B]_1^3\), the ratio \(\frac{rate_2}{rate_1}=\frac{27k[A][B]_1^3}{k[A][B]_1^3}=27\).

Answer:

27